work/Rate-1

[guerrero]

In the "Mashburn" pharmaceutical company there are two machines - a machine that produces blue pills and a machine that produces red pills. The machines are operated 10 hours a day, and the daily quota of the "blue" machine is 20% greater than that of the red machine. "¨If the "blue" machine was switched on at 8:00 and the "red" machine at 10:45, at what time will half of the combined daily quota be manufactured?

a) 13:15
b) 14:15
c) 14:30
d) 15:40
e) 19:15

OA B

[GMATGuruNY]

In the "Mashburn" pharmaceutical company there are two machines - a machine that produces blue pills and a machine that produces red pills. The machines are operated 10 hours a day, and the daily quota of the "blue" machine is 20% greater than that of the red machine. "¨If the "blue" machine was switched on at 8:00am and the "red" machine at 10:45am, at what time will half of the combined daily quota be manufactured?

a) 1:15pm
b) 2:15pm
c) 2:30pm
d) 3:40pm
e) 7:15pm

OA B

I've changed the times to reflect how they would appear on the GMAT.

Let R = the red machine and B = the blue machine.
Each machine produces its daily quota in 10 hours.
Let R's rate = 10 units per hour.
Since B's quota is 20% greater, let B's rate = 12 units per hour.
Total units produced by R and B in 10 hours = (combined rate)(time) = (10+12)(10) = 220 units.

B starts to work at 8am; R starts to work at 10:45am.
The question stem asks at what time half the daily quota -- in other words, 110 units -- will be produced.
We can plug in the answers for the time.

Answer choice C: 2:30pm
Work produced by B in 13/2 hours from 8am to 2:30pm = r*t = (12)(13/2) = 78 units.
Work produced by R in 15/4 hours from 10:45am to 2:30pm = r*t = (10)(15/4) = 37.5 units.
Total work produced = 78+37.5 = 115.5 units.
Since just a bit too much work is being produced, the two machines must work for just a bit less time.

The correct answer is B.

[Atekihcan]

Let us assume that daily quota of the red machine is 100 pills.
So, daily quota of the blue machine is 120 pills.
So, half of combined daily quota = (100 + 120)/2 = 110

Now, in one hour, the red machine produces 10 pills and the blue machine produces 12 pills.

Let's say after x hours from 10:45, half of the combined daily quota will be manufactured.
So, the blue machine will run for (x + 10:45 - 8:00) = (x + 2 + 3/4) = (x + 11/4) hours and the red machine will run for x hours.

In (x + 11/4) hours, the blue machine will produce 12(x + 11/4) pills and in x hours red machine will produce 10x pills.

So, 12(x + 11/4) + 10x = 110
--> 22x = 110 - 33 = 77
--> x = 77/22 = 7/2

7/2 hours = 3 hours + 30 minutes

(10:45 + 3 hours 30 minutes) = 14:15

Answer : B